Simulate a latent profile model — simulate

Draws each observation from a multivariate normal mixture: a profile is sampled from proportions, then the indicators are drawn from that profile's means, standard deviations and within-profile correlation matrix.

Usage

simulate_lpa(
  n,
  means,
  sds = 1,
  proportions = NULL,
  correlations = NULL,
  labels = NULL,
  seed = NULL,
  batch = NULL
)

Arguments

n: Number of observations. A single whole number of at least 2.
means: Profile-by-variable mean matrix (one row per profile, one column per indicator, at least 2 rows), or a tidy data frame with columns profile, variable and mean. Column names become the indicator columns of the returned data; row names, or the profile values of a tidy table, name the profiles unless labels is given.
sds: Scalar (the default, 1), per-variable vector, profile-by-variable matrix, or a tidy data frame with columns profile, variable and sd. All values must be positive.
proportions: Profile proportions, one positive value per profile; they are rescaled to sum to one. NULL (the default) makes every profile equally likely.
correlations: Optional list of within-profile correlation matrices, one per profile, or a tidy data frame with columns profile, row, column and correlation. NULL (the default) makes the indicators uncorrelated within every profile.
labels: Optional profile labels, one unique value per profile. Defaults to the profile names given with means (the profile values of a tidy table, or the row names of a matrix), else "Profile 1", "Profile 2" and so on.
seed: Optional random seed.
batch: Optional single positive whole number. When given, the simulator runs batch times and returns a plain list of batch results, each exactly what the same call without batch returns. With a seed, every dataset gets its own seed drawn from seed, so the whole batch is reproducible; without one the datasets are consecutive draws from the session's random-number stream. The default NULL returns a single result.

Value

A simulab_sim base data.frame with one row per observation and columns id, profile (the true profile label) and one numeric column per indicator. A parameters component holds one row per profile-by-variable combination with columns profile, variable, mean, sd and proportion.

Examples

# `means` is one row per profile and one column per indicator.
result <- simulate_lpa(
  n = 200,
  means = matrix(c(0, 0, 3, 3), nrow = 2, byrow = TRUE),
  proportions = c(0.6, 0.4),
  seed = 1
)
head(result)
#> <simulab_sim:lpa> 6 rows x 4 columns
#>   id   profile indicator_1 indicator_2
#> 1  1 Profile 1 -0.62036668 -1.25328976
#> 2  2 Profile 1  0.04211587  0.64224131
#> 3  3 Profile 1 -0.91092165 -0.04470914
#> 4  4 Profile 2  2.66571864  2.74883541
#> 5  5 Profile 1  0.15802877 -1.73321841
#> 6  6 Profile 2  3.73275004  1.57000655
#> 
#> Truth (parameters):
#>     profile    variable mean sd proportion
#> 1 Profile 1 indicator_1    0  1        0.6
#> 2 Profile 2 indicator_1    3  1        0.4
#> 3 Profile 1 indicator_2    0  1        0.6
#> 4 Profile 2 indicator_2    3  1        0.4
as.data.frame(result, what = "parameters")
#>     profile    variable mean sd proportion
#> 1 Profile 1 indicator_1    0  1        0.6
#> 2 Profile 2 indicator_1    3  1        0.4
#> 3 Profile 1 indicator_2    0  1        0.6
#> 4 Profile 2 indicator_2    3  1        0.4